Adding random thickness around a mesh
For the object you have in the picture, you can add two displace modifiers with a noise or clouds texture. Set one to effect the Y direction and the other to effect the X direction. Make sure Space is set to global.



You might like the results better if you first made a flat, segmented  rectangle shape, then use a displace in only the x axis (Local Space this time), subdivide it, solidify it, and then use a curve modifier to modify the object like below. You can mess around with different displacement textures and amounts to get the look you're after.